Octree Algorithm Research Articles

An efficient nonlocal integral method based on the octree algorithm

The nonlocal integral method typically requires a very high computing cost to search neighborhood integration points for calculating the nonlocal variable, which limits its application in large-scale problems. This paper proposes an efficient nonlocal integral method based on the octree algorithm, in which the integration point information is stored in the tree data structure to accelerate the search task. Firstly, the fundamental principles and implementation details of using the octree algorithm to search neighborhood integration points are described in detail. Subsequently, a Mohr-Coulomb nonlocal damage plastic model is presented as the application object of the proposed method. The model is implemented further in the ABAQUS using the octree-based nonlocal method and the return mapping algorithm enhanced by a line search method. Finally, two typical boundary value problems are simulated to verify the effectiveness and to assess the computational efficiency of the proposed nonlocal method. For the given test environment, the octree algorithm can achieve up to 100 times speedup at the integration point level compared to the traversal algorithm, and the developed efficient nonlocal method can achieve up to 7.9 times speedup at the boundary value problem level compared to the original nonlocal method.

An integrated simulation method for large‐scale earthquake‐induced falling debris in building groups

AbstractWhen building groups are subjected to earthquakes, the potential hazard of exterior falling debris poses a significant risk of causing severe injuries and fatalities. In this study, an integrated simulation method of the large‐scale earthquake‐induced exterior falling debris for building groups is proposed, which includes modeling, calculation, and visualization. Firstly, a modeling algorithm is established for falling debris models of building groups. This algorithm employs the Octree algorithm to support the transformation of the three‐dimensional (3D) building surface model into falling debris models. Subsequently, the generated falling debris models are aggregated using a density clustering algorithm, and their motion is efficiently calculated based on the physics engine and time history analysis. Finally, a cooperative visualization algorithm is developed to effectively present a 3D scene that incorporates both structural displacement and the motion of falling debris in building groups. The actual distribution of exterior falling debris during the earthquake in Turkey validates the proposed simulation method, which is then integrally applied to the Beijing central business district. This integrated simulation method has the capability to provide a large‐scale 3D scene of falling debris for the virtual safety drills of earthquake evacuation and rescue within urban building groups.

Research on Crop 3D Model Reconstruction Based on RGB-D Binocular Vision

Taking maize seedlings as the object, the implementation of crops 3D reconstruction based on RGB-D binocular vision and the selection of some key parameters are investigated in this research. First, multiple images are taken from different angles around the target. By mapping the maize seedling region coordinate values after the Otsu algorithm and global threshold segmentation to the corresponding depth image, the depth data of the maize seedling region can be obtained accurately. An improved mean filter is proposed to adaptively fill the holes in the depth image. Then, the different point clouds with the fixed step angle of the maize seedling are registered and fuzed. Finally, after the fusion point cloud is simplified, the 3D model of crops can be reconstructed. Experimental results show that the simplification effect of the octree algorithm is better than that of the voxel grid filter. Among all the step angles, the reconstruction error of the step angle with 60° is the smallest. Under this condition, the height error between the model and the maize seedling is 2.22%, and the error in stem diameter is 11.67%.

A Modeling Method of Graded Porous Scaffold Based on Triply Periodic Minimal Surfaces

In order to solve the design and regulation problems of graded porous scaffolds, the triply periodic minimal surface (TPMS) that based on implicit function was taken as the pore unit for constructing the porous scaffolds. And the TPMS structure was controlled by selecting different types of TPMS and defining the distance function. The transition of different structures of TPMS was performed by the weight fusion method. And the dual contouring (DC) algorithm and octree algorithm were used to divide the solid model of the defect bone into hexahedral elements to determine the target assembly spatial. Through the coordinate transformation of the isoparametric element method, the pore units were mapped into the hexahedral elements to construct porous structure. Finally, a Boolean operation was used to obtain a bone scaffold model with porous structure. The examples showed that the gradient model of various irregular pores could be constructed, and the pore size, porosity, and specific surface area of porous scaffolds could be controlled by adjusting the deformation, distribution, volume of the hexahedral elements, and the structure of the TPMS pore units, which provides a feasible method for the design and regulation of heterogeneous porous scaffolds.

Fast 2.5D and 3D inversion of transient electromagnetic surveys using the octree-based finite-element method

Two efficient implementations of 3D and 2.5D modeling and inversion are presented to be applicable to large-scale transient electromagnetic (TEM) method explorations. The key novel features are (1) forward response and Jacobian calculations are implemented using the octree-based finite-element method, (2) a mirror approach is used to build a 2.5D inversion scheme for further efficiency, and (3) a flexible link between the forward mesh and inversion model is applied on 3D and 2.5D schemes based on the voxel formulation. We compare the performance of the new implementations with 3D modeling using tetrahedral meshes, with respect to speed and memory requirements. The 3D octree algorithm requires less than 1/3 of the computational time compared with a 3D tetrahedral scheme for equivalent accuracy. The 2.5D octree algorithm further speeds up the process by reducing the computational time by another factor of two. The inversion uses the Levenberg-Marquart approach minimizing the least-squares criterion of the objective function. We determine the utility of our inversion approach on a synthetic example and a field example. In the synthetic example, the 3D octree inversion result finds superior resolution of a 3D anomaly compared with a 1D result, whereas the 2.5D inversion result is, expectedly, between the 1D and 3D results, but with favorable computational expenses compared with the full 3D solution. The field data set contains 200 soundings, and we perform a 3D inversion on the full survey. A 24-sounding section is then selected for the 2.5D inversion. The 2.5D inversion result finds resistivity features similar to the 3D inversion result at the selected profile. Hence, we conclude that the presented implementations are capable of handling relatively large TEM surveys on modern computational platforms. This could be smaller subsets of production-size surveys where 2D and 3D effects are pronounced.

Material Removal Optimization Strategy of 3D Block Cutting Based on Geometric Computation Method

During the material removal stage in stone rough processing, milling type has been widely explored, which, however, may cause time and material consumption, as well as substantial stress for the environment. To improve the material removal rate and waste reuse rate in the rough processing stage for three-dimensional stone products with a special shape, in this paper, circular saw disc cutting is explored to cut a convex polyhedron out of a blank box, which approaches a target product. Unlike milling optimization, this problem cannot be well solved by mathematical methods, which have to be solved by geometrical methods instead. An automatic block cutting strategy is proposed intuitively by considering a series of geometrical optimization approaches for the first time. To obtain a big removal block, constructing cutting planes based on convex vertices is uniquely proposed. Specifically, the removal vertices (the maximum thickness of material removal) are searched based on the octree algorithm, and the cutting plane is constructed based on this thickness to guarantee a relatively big removal block. Moreover, to minimize the cutting time, the geometrical characteristics of the intersecting convex polygon of the cutting plane with the convex polyhedron are analyzed, accompanied by the constraints of the guillotine cutting mode. The optimization algorithm determining the cutting path is presented with a feed direction accompanied by the shortest cutting stroke, which confirms the shortest cutting time. From the big removal block and shortest cutting time, the suboptimal solution of the average material removal rate (the ratio of material removal volume to cutting time) is generated. Finally, the simulation is carried out on a blank box to approach a bounding sphere both on MATLAB and the Vericut platform. In this case study, for the removal of 85% of material with 19 cuts, the proposed cutting strategy achieves five times higher the average material removal rate than that of one higher milling capacity case.

A Study on the Whole-skin Peeling System of a Snakehead Based on Three-dimensional Reconstruction

HighlightsA 3D reconstruction algorithm is proposed to determine the snakehead area.The whole-skin peeling system of snakehead is designed by a convolutional neural network.An automatic whole-skin peeling device is presented with computer vision technology.Abstract. A whole-skin peeling system for a snakehead is designed in this article. The snakehead photos are taken from multiple angles and are first filtered to extract the image features, before reconstructing the sparse model. Then, the characteristic parameters of the snakehead are determined through the point cloud coordinates, and dense reconstruction is carried out based on sparse points. The accurate three-dimensional spatial coordinates of the snakehead are obtained by the octree algorithm and Poisson surface reconstruction algorithm. Based on the triangular meshing algorithm, the skin area of a snakehead is calculated to determine whether the snakehead meets the peeling conditions. A trained Faster Region Convolutional Neural Network (R-CNN) is used to identify the fin position on the snakehead reconstruction model and program the cutting route on the fish neck, while the cutting route of the fish belly is determined by selecting the area of the excretory hole through the ROI region of interest. Finally, the designed mechanical structure is used to peel the whole skin of the snakehead. The experimental results show that the maximum fluctuation rate of the snakehead area calculated by the proposed three-dimensional reconstruction algorithm is less than 4.0%, and the accuracy reaches 87.3%. The average precision (AP) for the determination method of the fish neck cutting position on the snakehead is 90.89%, which proves the effectiveness and feasibility of this method. The present results provide useful technical support for automating fish whole-skin peeling and shedding light on the accurate determination of the surface area and the extrication of the morphological feature parameters of other organisms. Keywords: Neural network, Point cloud, Snakehead, Skin peeling, Three-dimensional reconstruction.

Shortest Path Selection Algorithm for Cold Chain Logistics Transportation Based on Improved Artificial Bee Colony

Aiming at the problems of low shortest path selection accuracy, longer response time, and poor selection effect in current cold chain logistics transportation methods, a cold chain logistics transportation shortest path selection algorithm based on improved artificial bee colony is proposed. The improved algorithm is used to initialize the food source, reevaluate the fitness value of the food source, generate a new food source, optimize the objective function and food source evaluation strategy, and get an improved artificial bee colony algorithm. Based on the improved artificial bee colony algorithm, the group adaptive mechanism of particle swarm algorithm is introduced to initialize the position and velocity of each particle randomly. Dynamic detection factor and octree algorithm are adopted to dynamically update the path of modeling environment information. According to the information sharing mechanism between individual particles, the group adaptive behavior control is performed. After the maximum number of cycles, the path planning is completed, the shortest path is output, and the shortest path selection of cold chain logistics transportation is realized. The experimental results show that the shortest path selection effect of the cold chain logistics transportation of the proposed algorithm is better, which can effectively improve the shortest path selection accuracy and reduce the shortest path selection time.

A polyhedral element formulation based on the scaled boundary method for the analysis of nonlinear problems in solid mechanics

AbstractIn this contribution a numerical element formulation for the nonlinear analysis of solids is proposed. The element is defined by a polyhedron with an arbitrary number of polygonal faces. It is based on the scaling concept, which is adopted from the so‐called scaled boundary finite element method (SBFEM). The SBFEM is a semi‐analytical formulation to analyze problems in linear elasticity. Within this method the fundamental concept is to scale the domain's boundary with respect to a scaling center in order to describe the interior domain. The present element formulation employs the scaling concept twice and in contrast to SBFEM, uses a numerical approximation for the displacement response in both scaling directions. This makes it suitable for the analysis of geometrically and physically nonlinear problems. The advantages of the proposed element formulation is its high flexibility in mesh generation. It avoids the hanging node problems as arbitrary element geometries are possible. For example, using Octree algorithms, a fast and reliable mesh generation can be achieved. In case of curved boundaries the element formulation allows a precise representation of the geometry even with coarse meshes. Some numerical examples are presented to evaluate the accuracy of the proposed numerical method against analytical solutions, and a comparison to standard element formulations is given as well.

A novel adaptive mesh refinement scheme for the simulation of phase‐field fracture using trimmed hexahedral meshes

AbstractIn this article, a novel adaptive mesh refinement scheme based on trimmed hexahedral (TH) meshes is proposed to simulate phase‐field fracture in brittle materials. A regular hexahedral background mesh is adaptively refined using a balanced octree algorithm to resolve the length scale in phase‐field fracture models. Adaptively refined TH meshes are created by cutting octree background meshes with the boundary of an analysis domain. A multithreshold criterion for mesh refinement is proposed to accurately capture the evolution of the damage phase field. Shape functions for transition TH elements are developed to satisfy the compatibility across the interelement boundaries between TH elements with different refinement levels. Numerical results show that the present scheme is very efficient and effective to trace arbitrary evolving phase‐field cracks in three dimensions.

Automated simulation of voxel-based microstructures based on enhanced finite cell approach

A new and efficient method is proposed for the decomposition of finite elements into finite subcells, which are used to obtain an integration scheme allowing to analyse complex microstructure morphologies in regular finite element discretizations. Since the geometry data of reconstructed microstructures are often given as voxel data, it is reasonable to exploit the special properties of the given data when constructing the subcells, i.e. the perpendicularly cornered shape of the constituent interfaces at the microscale. Thus, in order to obtain a more efficient integration scheme, the proposed method aims to construct a significantly reduced number of subcells by aggregating as much voxels as possible to larger cuboids. The resulting methods are analysed and compared with the conventional Octree algorithm. Eventually, the proposed optimal decomposition method is used for a virtual tension test on a reconstructed three-dimensional microstructure of a dual-phase steel, which is afterwards compared to real experimental data.

An Efficient Encoding Voxel-Based Segmentation (EVBS) Algorithm Based on Fast Adjacent Voxel Search for Point Cloud Plane Segmentation

Plane segmentation is a basic yet important process in light detection and ranging (LiDAR) point cloud processing. The traditional point cloud plane segmentation algorithm is typically affected by the number of point clouds and the noise data, which results in slow segmentation efficiency and poor segmentation effect. Hence, an efficient encoding voxel-based segmentation (EVBS) algorithm based on a fast adjacent voxel search is proposed in this study. First, a binary octree algorithm is proposed to construct the voxel as the segmentation object and code the voxel, which can compute voxel features quickly and accurately. Second, a voxel-based region growing algorithm is proposed to cluster the corresponding voxel to perform the initial point cloud segmentation, which can improve the rationality of seed selection. Finally, a refining point method is proposed to solve the problem of under-segmentation in unlabeled voxels by judging the relationship between the points and the segmented plane. Experimental results demonstrate that the proposed algorithm is better than the traditional algorithm in terms of computation time, extraction accuracy, and recall rate.

An approach integrating BIM, octree and FEM-SBFEM for highly efficient modeling and seismic damage analysis of building structures

This paper presents a novel BIM-Octree-FEM-SBFEM method (BOFSM) for rapid modeling and seismic damage analysis of structures. The BOFSM enables rapid and accurate modeling of structures by incorporating three innovative improvements. Firstly, integrating the digital building information method (BIM) with the Octree algorithm for discretization, a complex geometric model can be directly transformed into an analysis model. The automated transformation process eliminates considerable manual efforts typically expended in the traditional method. Secondly, the solver is improved using finite element method (FEM) to solve the hexahedrons elements while using scaled boundary FEM (SBFEM) to solve the polyhedrons. Thirdly, a nonlinear similar element (NSE) technique is proposed for cubes that occupy about 80% of the meshes. The matrices of one unit cubic element are pre-computed and stored in memory. Subsequently, the parameters of each element can be directly computed by scaling the dimensional coefficient and damage factor, thus offering an economical computational approach for massive matrices in damage analyses. The above methods are implemented in an in-house program GEODYNA, with CPU+GPU parallelization and multitasking capacity. Two refined seismic destruction analyses for frame buildings were conducted and some potential advantages are discussed. The results demonstrate the efficiency, universality and robustness of the BOFSM.

Implementation of CUDA-based Octree Algorithm for Efficient Search for LiDAR Point Cloud

Implementation of CUDA-based Octree Algorithm for Efficient Search for LiDAR Point Cloud

3D VISUALIZATION OF VOLCANIC ASH DISPERSION PREDICTION WITH SPATIAL INFORMATION OPEN PLATFORM IN KOREA

Abstract. Visualization of disaster dispersion prediction enables decision makers and civilian to prepare disaster and to reduce the damage by showing the realistic simulation results. With advances of GIS technology and the theory of volcanic disaster prediction algorithm, the predicted disaster dispersions are displayed in spatial information. However, most of volcanic ash dispersion predictions are displayed in 2D. 2D visualization has a limitation to understand the realistic dispersion prediction since its height could be presented only by colour. Especially for volcanic ash, 3D visualization of dispersion prediction is essential since it could bring out big aircraft accident. In this paper, we deals with 3D visualization techniques of volcanic ash dispersion prediction with spatial information open platform in Korea. First, time-series volcanic ash 3D position and concentrations are calculated with WRF (Weather Research and Forecasting) model and Modified Fall3D algorithm. For 3D visualization, we propose three techniques; those are 'Cube in the air', 'Cube in the cube', and 'Semi-transparent plane in the air' methods. In the 'Cube in the Air', which locates the semitransparent cubes having different color depends on its particle concentration. Big cube is not realistic when it is zoomed. Therefore, cube is divided into small cube with Octree algorithm. That is 'Cube in the Cube' algorithm. For more realistic visualization, we apply 'Semi-transparent Volcanic Ash Plane' which shows the ash as fog. The results are displayed in the 'V-world' which is a spatial information open platform implemented by Korean government. Proposed techniques were adopted in Volcanic Disaster Response System implemented by Korean Ministry of Public Safety and Security.

3D VISUALIZATION OF VOLCANIC ASH DISPERSION PREDICTION WITH SPATIAL INFORMATION OPEN PLATFORM IN KOREA

Visualization of disaster dispersion prediction enables decision makers and civilian to prepare disaster and to reduce the damage by showing the realistic simulation results. With advances of GIS technology and the theory of volcanic disaster prediction algorithm, the predicted disaster dispersions are displayed in spatial information. However, most of volcanic ash dispersion predictions are displayed in 2D. 2D visualization has a limitation to understand the realistic dispersion prediction since its height could be presented only by colour. Especially for volcanic ash, 3D visualization of dispersion prediction is essential since it could bring out big aircraft accident. In this paper, we deals with 3D visualization techniques of volcanic ash dispersion prediction with spatial information open platform in Korea. First, time-series volcanic ash 3D position and concentrations are calculated with WRF (Weather Research and Forecasting) model and Modified Fall3D algorithm. For 3D visualization, we propose three techniques; those are 'Cube in the air', 'Cube in the cube', and 'Semi-transparent plane in the air' methods. In the 'Cube in the Air', which locates the semitransparent cubes having different color depends on its particle concentration. Big cube is not realistic when it is zoomed. Therefore, cube is divided into small cube with Octree algorithm. That is 'Cube in the Cube' algorithm. For more realistic visualization, we apply 'Semi-transparent Volcanic Ash Plane' which shows the ash as fog. The results are displayed in the 'V-world' which is a spatial information open platform implemented by Korean government. Proposed techniques were adopted in Volcanic Disaster Response System implemented by Korean Ministry of Public Safety and Security.

Computation of streaming potential in porous media: Modified permeability tensor

We quantify the pressure-driven electrokinetic transport of electrolytes in porous media through a matched asymptotic expansion based method to obtain a homogenized description of the upscaled transport. The pressure driven flow of aqueous electrolytes over charged surfaces leads to the generation of an induced electric potential, commonly termed as the streaming potential. We derive an expression for the modified permeability tensor, K↔eff, which is analogous to the Darcy permeability tensor with due accounting for the induced streaming potential. The porous media herein are modeled as spatially periodic. The modified permeability tensor is obtained for both topographically simple and complex domains by enforcing a zero net global current. Towards resolving the complicated details of the porous medium in a computationally efficient framework, the domain identification and reconstruction of the geometries are performed using adaptive quadtree (in 2D) and octree (in 3D) algorithms, which allows one to resolve the solid–liquid interface as per the desired level of resolution. We discuss the influence of the induced streaming potential on the modification of the Darcy law in connection to transport processes through porous plugs, clays and soils by considering a case-study on Berea sandstone.

Comparison of efficient techniques for the simulation of dielectric objects in electrolytes

We review two recently developed efficient approaches for the numerical evaluation of the electrostatic polarization potential in particle-based simulations. The first is an image-charge method that can be applied to systems of spherical dielectric objects and provides a closed-form solution of Poisson's equation through multiple image-charge reflections and numerical evaluation of the resulting line integrals. The second is a boundary-element method that computes the discretized surface bound charge through a combination of the generalized minimal residual method (GMRES) and a fast Ewald solver. We compare the accuracy and efficiency of both approaches as a function of the pertinent numerical parameters. We demonstrate use of the image-charge method in a Monte Carlo simulation using the Barnes–Hut octree algorithm and the boundary-element method in a molecular dynamics simulation using the Particle–Particle Particle–Mesh (PPPM) Ewald method, and present numerical results for the ensemble-averaged induced force between two spherical colloids immersed in an electrolyte.

Efficient implementation of the Barnes-Hut octree algorithm for Monte Carlo simulations of charged systems

Computer simulation with Monte Carlo is an important tool to investigate the function and equilibrium properties of many systems with biological and soft matter materials solvable in solvents. The appropriate treatment of long-range electrostatic interaction is essential for these charged systems, but remains a challenging problem for large-scale simulations. We have developed an efficient Barnes-Hut treecode algorithm for electrostatic evaluation in Monte Carlo simulations of Coulomb many-body systems. The algorithm is based on a divide-and-conquer strategy and fast update of the octree data structure in each trial move through a local adjustment procedure. We test the accuracy of the tree algorithm, and use it to perform computer simulations of electric double layer near a spherical interface. It has been shown that the computational cost of the Monte Carlo method with treecode acceleration scales as $\log N$ in each move. For a typical system with ten thousand particles, by using the new algorithm, the speed has been improved by two orders of magnitude from the direct summation.

The Filtering and Streamline of Three-Dimensional Point-Cloud Data

Three-dimensional scanning device will scan a large number of three-dimensional data one time, which will inevitably mixed with some of the noise points, casusing the reconstructed surfaces and curves that is not smooth. At the same time a large number of three-dimensional data can lead to reconstructing surface slow down. This paper applied Wiener-filtering which is commonly used in the gray image de-noising and smoothing treatment to filtering three-dimensional point-cloud-data by replace the gray value of gray image with a z value of point-cloud-data, and the point-cloud-data which undulates strongly will be seen as noise point and removed. At the same time using octree algorithm to streamline the data, which can be guaranteed to retain local feature point cloud data while streamlining data.